Following the developments in quantum theory of gravity, the
motivation to solve the DE problem, including its nature and
behavior, has arisen a lot of attentions [1]}. An example
of such effort is the HDE models
[2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. The area-entropy relation is the backbone of this
hypothesis claiming that black hole relates the short distance
cutoff to the long distance cutoff, which leads to an upper bound
for the zero-point energy density [2]}. Based on this
theory, we have \(\rho _D=3c^2M_p^2L^{-2}\)  for the energy density of
HDE, where \(c^2\)  and \(L\)  are, respectively, a constant and the
infrared (IR) cutoff, and \(M_{p}\)  is the reduced Planck mass
[3]}, [4]}. One of the basic assumption in the HDE
models is the suitable IR cutoff which leads to an accelerated
universe. The simplest choice for the IR cutoff is the Hubble
radius which is defined as, \(L=H^{-1}\) . However, it was argued
that Hubble radius cannot lead to an accelerating universe
[3]}, unless the interaction between DE and DM is taken
into account [5]}, [6]}. In 2008, Granda and
Oliveros (GO) proposed a combination of the Hubble parameter and
its first derivative as the IR cutoff of HDE models, namely
\(L=(\alpha H^2+\beta \dot{H})^{-1/2}\)  where \(\alpha \)  and \(\beta \) 
are constant [15]}, [16]}. This cutoff which is
known as the GO cutoff avoids the causality problem and solves the
coincidence problem and extensively investigated in the
literatures [17]}, [18]}.
